The Nets may not re-sign Deron Williams this summer, but it won’t be for a lack of trying.

The star point guard, who repeatedly has said he will opt out of the final year of his contract to test free agency this summer, spent yesterday in Istanbul, Turkey with Nets general manager Billy King and, as first reported by The Post, owner Mikhail Prokhorov.

It only can be seen as a good sign for the Nets that Williams would choose to spend time with King and Prokhorov during the offseason.

With Williams officially under contract until June 30 — the deadline for when he has to decide to exercise the early termination option in his deal — the Nets have a two-month head start on the competition to show Williams he should remain with the franchise and be the face of the team’s transition to Brooklyn this fall.

Last week, King said he would be in Istanbul for this weekend’s Euroleague Final Four so he could meet with the Nets’ second-round pick in 2011, swingman Bojan Bogdanovic. Though it wasn’t known Williams was planning on making the trip, as well, it makes sense. He spent last fall playing in Istanbul for Turkish power Besiktas during the lockout.

Williams was one of the lone stars to agree to play overseas during the work stoppage, and has talked openly about how much he enjoyed his time there. Istanbul is only a few hours by plane away from Prokhorov’s home in Moscow.

The three men were on hand for the first of yesterday’s two Euroleague semifinals, watching Andrei Kirilenko lead CSKA Moscow, Prokhorov’s former team, to a hard-fought 66-64 win over Panathinaikos to advance to tomorrow’s final. Kirilenko finished with 17 points, nine rebounds and four blocks for CSKA, and has an extensive history with Williams and Prokhorov.

Kirilenko and Williams were teammates with Utah from 2005 — when the Jazz drafted Williams — until they traded him to the Nets at the trading deadline in 2011. Instead of trying to return to the NBA this season, Kirilenko, who endorsed Prokhorov’s failed Russian presidential bid, decided to play for CSKA, where he played from 1998 to 2001 before going to Utah.

He went on to have a terrific season for CSKA, widely considered the best team in the world outside of the NBA and a heavy favorite to win the Euroleague title this weekend.

Considered one of the most versatile players in the NBA during his time with Utah, Kirilenko averaged 14.2 points, 7.3 rebounds, 2.5 assists, 1.4 steals and 2.0 blocks while shooting 59 percent from the field and 40 percent from 3-point range in Euroleague competition.

Multiple sources shot down a report last week that the Nets are nearing a verbal agreement with Kirilenko, but also said the Nets have monitored his performance this season.

If King and Prokhorov can convince Williams to re-sign, they will have plenty of room to augment the roster to their star’s desire. Only four Nets — guards Anthony Morrow and MarShon Brooks, forward Jordan Williams and center Johan Petro — currently have contracts for next season.